It is often necessary or desirable to limit heat transfer from an object to its surroundings. Heat transfer is the transfer of energy resulting from a temperature differential between the object and its surroundings. Heat transfer occurs through three fundamental mechanisms: radiation, conduction (solid and gas) and convection.
Conduction generally involves the transfer of energy of motion between adjacent molecules, such as vibration of atoms in a crystal lattice or random motion of molecules in a gas. As such, conduction requires physical contact to effect heat transfer. Steady-state conduction in solids is generally represented by Fourier's equation:q=−kAdt/dx where:                q=heat-conduction rate in the x direction        A=cross-sectional area normal to heat flow        dt/dx=temperature gradient in the x direction        k=thermal conductivity of the conducting medium        
The thermal conductivity, k, is a function of the molecular state of the conducting medium. Accordingly, it is generally considered to be dependent upon temperature and pressure. Lower values of k result in a reduction in heat transfer. Heat transfer occurs in the direction of decreasing temperature.
From the kinetic theory of gases, the energy transfer rate by conduction through gases, or molecular conduction, can be determined as:q=GPA1(t2−t1)where:                G=[(γ+1)/(γ−1)](gcR/8πT)1/2Fa         R=specific gas constant        Fa=accommodation coefficient factor        P=absolute pressure        t1=temperature of the absorbing surface        t2=temperature of the conducting surface        T=temperature of the gas separating the conducting and absorbing surfaces        A1=cross-sectional area of the absorbing surface normal to heat flow        
In reference to the above function for gas conduction, the mean free path, λ, must be larger than the spacing of the absorbing and conducting surfaces, where:λ=(μ/P)(πRT/2gc)1/2 where: μ=gas viscosity
Convection involves the transfer of heat due to bulk transport and mixing of macroscopic elements of a fluid. Convection is thus more complicated than conduction as fluid dynamics play a significant factor in the rate of heat transfer. Steady-state convective heat transfer may be simplified to an equation of the form:q=hA(ts−tm)where:                q=heat-transfer in the direction of decreasing temperature        h=convective heat-transfer coefficient        A=cross-sectional area normal to heat flow        ts=surface temperature of the conducting object        tm=temperature of the surrounding fluid medium some distance from the object surface        
The heat-transfer coefficient, h, is a function of the properties of the fluid, the geometry and surface characteristics of the object surface, and the flow pattern of the fluid. Convection can by induced by density differences within the fluid medium, i.e., natural convection, or motion may be the result of external forces, i.e., forced convection. Because convective heat transfer relies on transport within a fluid medium, this component can often be ignored at pressures below about 50 torr.
Radiation is the transfer of heat by electromagnetic radiation, or photons. Radiation transfer is dependent upon the absorptivity, emissivity and reflectivity of the body radiating energy, i.e., the source, and the body at which the radiation impinges, i.e., the sink. Steady-state radiation heat transfer may be simplified to an equation of the form:q=hrAs2(ts14−ts24)where:                q=heat-transfer in the direction of decreasing temperature        hr=radiation heat-transfer coefficient        A=cross-sectional area of the sink object normal to the radiation        ts1=surface temperature of the source object        ts2=surface temperature of the sink objectand: hr=FeF2→1σwhere:        Fe=emissivity factor        F2→1=configuration factor        σ=Stefan-Boltzman constant        
There is a strong dependence of the heat-transfer coefficient, hr, on temperature as an object's radiation, and thus the heat transfer medium, will depend largely on its temperature. Although radiation transfer may occur through gases, liquids or solids, these media will absorb or reflect some or all of the energy. Accordingly, radiation transfer occurs most efficiently through an empty, vacuous space.
One common thermal insulation used in cryogenic and aerospace applications is known as Multilayer Insulation (MLI), or Superinsulation. The development of MLI around 1960 was spurred on by the space program and generally contains multiple layers of reflective material separated by spacers having low conductivity.
Ideal MLI consists of many radiation shields stacked in parallel as close as possible without touching. Low thermal conductivity spacers are employed between the layers to keep the highly conductive shields from touching one another. MLI will typically contain on the order of 50 layers per inch. MLI is thus anisotropic by nature, making it difficult to apply to complex geometries. MLI is generally very sensitive to mechanical compression and edge effects, requiring careful attention to details during all phases of installation. Accordingly, performance in practice, even under laboratory conditions, is often several times worse than ideal.
In addition, MLI is designed to work under high vacuum levels, i.e., below about 1×10−4 torr. Not only does this require lengthy evacuation, purging and heating cycles to obtain such high vacuum levels for proper performance, but such systems require either dedicated pumping systems or adsorbents and chemical gettering packs to maintain their high vacuum. Furthermore, performance of MLI degrades rapidly upon loss of such high vacuum levels.
Another common insulation is foam insulation. Foam insulation requires no vacuum. Foams generally have reduced thermal conductivity given their relatively low densities. Furthermore, foams inhibit convective heat transfer by limiting convection to the individual cells, fissures or other spaces within the foam structure. Foam insulation generally includes some form of moisture barrier as moisture accumulation within the spaces of the foam structure will rapidly increase the thermal conductivity of the foam. Typical foam structures include polyurethane foam, polyimide foam and foam glass.
Foam insulation is generally not favored in cryogenic applications. Such insulation is prone to cracking due to thermal cycling and environmental exposure. Cracks permit incursion of moisture and humid air, which will form ice and greatly increase the surface area for heat transfer.
Other insulation systems useful in cryogenic applications include evacuated annular spaces having bulk-filled materials, e.g., glass fiber, silica aerogel or composites. As with MLI, these systems require high vacuum levels of around 1×10−3 torr. Additional insulation systems are well known in the art.
Cryogenic insulation system performance is often reported for large temperature differences in terms of an apparent thermal conductivity, or k value. Boundary temperatures of 77K (liquid nitrogen) and 290K (room temperature) are common. Unless otherwise noted, k values discussed herein apply generally to these boundary conditions.
MLI systems can produce k values of below 0.1 mW/m-K (R-value of approximately 1440) when properly operating at cold vacuum pressure (CVP) below about 1×10−4 torr. For bulk-filled insulation systems operating at CVP below about 1×10 −3 torr, k values of about 2 mW/1-K (R-value of approximately 72) may be typical. Foam and similar materials at ambient pressures typically may produce k values of about 30 (R-value of approximately 4.8). It should be noted that a k value of 1 mW/m-K is equivalent to an R-value of 144.2. R-value is a standard industry unit of thermal resistance for comparing insulating values of different materials. It is a measure of a material's resistance to heat flow in units of ° F.-hr-ft2/BTU-in. All values given as typical above represent one inch of insulation of the type described.
Insulation systems are known which have low thermal conductivities at high vacuum conditions, but their performance degrades precipitously as pressure is increased above 1×10−3 torr. Other insulation systems are capable of operating at ambient pressure, but do not exhibit sufficiently low thermal conductivity for most cryogenic applications and are difficult to protect against moisture and air intrusion. Accordingly, there is a need in the art for systems of thermal insulation having reasonably low thermal conductivity across a wide range of pressure and temperature conditions.